The endpoints of EF¯¯¯¯¯ are located at E (−3, 2) and F (3, 8). Point D divides EF¯¯¯¯¯ such that ED : DF is equal to 1 : 3. For each box, select the values in the dropdown that make the statement true. The x-coordinate of point D is and the y-coordinate of point D is

Answer:

[tex]D(x,y) = (-1.5,3.5)[/tex]

Step-by-step explanation:

Given

[tex]E = (-3,2)[/tex]

[tex]F = (3,8)[/tex]

[tex]ED: DF = 1 : 3[/tex]

Required

Determine the coordinates of D

This is calculated as thus:

[tex]D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

Where:

[tex](x_1,y_1) = (-3,2)[/tex]

[tex](x_2,y_2) = (3,8)[/tex]

[tex]m:n = 1:3[/tex]

[tex]D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

[tex]D(x,y) = (\frac{1 * 3 + 3 *-3}{1+3},\frac{1 * 8 + 3 * 2}{1+3})[/tex]

[tex]D(x,y) = (\frac{-6}{4},\frac{14}{4})[/tex]

[tex]D(x,y) = (-1.5,3.5)[/tex]

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